NEW YORK — As states begin or continue the process of allowing more businesses and public facilities to open, some members of the traveling public wonder how many trains Amtrak will run this summer. Amtrak is running fewer trains than ever on the Northeast Corridor (NEC) and other corridors, as part of the shutdown of much of the nation’s activity in response to the COVID-19 pandemic. At this writing, a few places have loosened some of the virus-related restrictions, while others are planning how and when to do so. Amtrak will probably return to a level of service approaching the schedule at the beginning of March someday, on some lines if not all of them, but nobody knows when. Apparently not even Amtrak is sure and, for some trains, Amtrak lacks the authority to make those decisions.